A synthetic phospholipid bilayer has thickness and its exposed hydrocarbon-water…

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Soft condensed matter · Soft condensed matter

Soft Matter at the Thermal Scale, Ch Amphiphiles and self-assembly

Problem

A synthetic phospholipid bilayer has thickness d=3.5 nmd = 3.5\,\mathrm{nm} and its exposed hydrocarbon-water interface has tension γhc=0.045 N m−1\gamma_{\rm hc} = 0.045\,\mathrm{N\,m^{-1}}. ((a)) Estimate the crude edge (line) energy per unit length, Λcrude≈γhcd/2\Lambda_{\rm crude} \approx \gamma_{\rm hc}d/2, treating the exposed rim as a strip of bare hydrocarbon-water interface half the bilayer thickness dd tall, as in the chapter's strip picture. ((b)) Measured pore line tensions in lipid bilayers are typically about ten times smaller than this crude estimate, because the rim lipids tilt to cover their tails. Estimate the actual edge tension Λ\Lambda. ((c)) Using this measured value, estimate the total edge energy, in units of kBTk_BT at 298 K298\,\mathrm{K}, of a flat circular bilayer patch of radius R=250 nmR = 250\,\mathrm{nm}.

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